Multiperiod Bus Timetabling

Abstract

The timetabling subproblem of bus transit network planning determines the departure times for all trips of the lines along the entire day. Most of the public transport networks consider planning periods identical for all lines. In this study we drop this strong assumption by introducing specific periods for each line, which is more realistic. Thus, we propose the multiperiod synchronization bus timetabling (MSBT) problem, which specifies the departure times of the trips of all lines where each line has its own planning periods along the day, with the objective of optimizing synchronization events: maximize passenger transfers and minimize bus bunching along the network. We propose an integer linear programming formulation for the MSBT problem and analyze the structural properties of this formulation by a constraint propagation methodology. These properties are the basis for different operators that lead to the design of efficient metaheuristics for solving the problem. We empirically obtain high-quality feasible solutions for real size instances and show that by considering a multiperiod approach, synchronization events of trips belonging to different planning periods are not ignored, as it is the case when several single period timetables are merged.

Linear Bus Holding Model for Real-Time Traffic Network Control

“…Then, variables h ks should be in seconds or in minutes and therefore integer variables. Preliminary results showed no drastic increment in the computing times when bus holding variables h ks are integer [1,4,6,15].…”

“…As mentioned, the headway is a quality measure given to the time difference between two consecutive buses. A bus line could have equally distant headways or different ones for each pair of buses Ceder [2], Ibarra-Rojas and Rios-Solis [14], Ibarra-Rojas et al [15]. We say that headways are congruent if the real-time differences between buses are nearly identical to the originally planned.…”

Transfer Coordination for Metro Networks during the Start- or End-of-Service Period

“…Based on this, Eranki [9] redefined synchronization as the simultaneous arrival of two buses within a time window and devised the corresponding heuristic approach. Ibarra-Rojas et al [10,11] also applied the concept of synchronization and developed different metaheuristic solving frameworks (iterated located search, variable neighborhood search, and evolutionary algorithm), whereas Fouilhoux et al [12] devised four classed of valid inequalities to cut fractional solutions of the linear relaxations of integer programs and nonoptimal feasible solutions, thereby yielding a shrink in the feasible space. Consequently, a promotion in solving efficiency is acquired when implementing the exact branch-and-cut algorithm in CPLEX.…”

Development of a model for determining the time parameters for the interaction of passenger transport in a suburban transport and transfer terminal

“…-allowance for stochastic motion [10]; -the number of passenger transfers [11]; -taking into account the periods of possible transfer of passengers [12]; -assessing transit flows [13]; -multi-criteria evaluation of the results [14]. A common disadvantage of the existing approaches to technological coordination of the interaction of transport in the TTT is that they do not take into account the potential possibilities to ensure a reduction in the time of passenger transfer by creating conditions for the simultaneous stay of vehicles in the TTT.…”